{% extends "homepage.html" %}

{% block content %}

{% if user_is_authenticated %}




{#

<form action="{{ url_for('.search') }}" method="GET">
<input name="val" placeholder="123" />
<button type="submit">Search</button>
</form>

<p>
HTML to be improved, not the priority. Need stuff defined a bit better so I know what I am trying to do and I can do it right.
</p>
<div>
This page is about {{KNOWL("artin",title="Artin representations")}} of the {{KNOWL("group.galois.absolute",title="absolute Galois group")}} over {{KNOWL("group.galois.absolute.q",title="$Q$")}} of 
</div>

<div>
Terms that need to be defined are
<p>
{{KNOWL("artin",title="Artin representations")}}
</p>

<p>
<div>{{KNOWL("artin.degree",title="Degree")}}</div>
<div>{{KNOWL("artin.number_field",title="Artin number field")}}</div>
<div>{{KNOWL("artin.galois_group",title="Galois group")}}</div>
<div>{{KNOWL("artin.dimension",title="Dimension")}}</div>
<div>{{KNOWL("artin.conductor",title="Conductor")}}</div>
<div>{{KNOWL("artin.root_number",title="Root number")}}</div>
<div>{{KNOWL("artin.ramification_group",title="Ramification group")}}</div>
</p>

<h2> Find</h2>
Find Artin representation by <div>{{KNOWL("artin.conductor",title="conductor")}}</div>

<form action="" method=get>
<p>
<input type='submit' value='Find' >
</p>
</form>
#}

{# {{ info.query }} #}






<div>
{{KNOWL_INC("artin", title = "")}}
</div>
<div>
As a preview, the LMFDB database currently contains a few hundred Artin representations, each factoring through a Galois group of relatively small order.
These representations were all computed in Magma by Tim Dokchitser, and the list is currently not meant to be exhaustive in any way.
<br>
<br>
Soon one will also be able to access information about the associated {{KNOWL("artin.lfunction", title = "Artin L-function")}}. 
</div>

<h2> Browse Artin representations</h2>

<p>
By {{ KNOWL('ec.q.conductor',title = "conductor")}}:
<a href="?conductor={{'1-99'}}">{{'1-99'}}</a>
<a href="?conductor={{'100-199'}}">{{'100-199'}}</a>
<a href="?conductor={{'200-299'}}">{{'200-299'}}</a>
<a href="?conductor={{'300-399'}}">{{'300-399'}}</a>
</p>
<p>
By {{ KNOWL('ec.q.rank', title="rank")}}:
{% for r in info.rank_list: %}
<a href="?rank={{r}}">{{r}}</a>
{% endfor %}
</p>
<p>
By {{ KNOWL('ec.q.torsion_order', torsion=t,title="torsion order") }}:
{% for t in info.torsion_list: %}
<a href="?torsion={{t}}">{{t}}</a>
{% endfor %}
</p>


<h2> Search for an Artin representation </h2>
Please enter a value or leave blank:
<p></p>
<form>
  <table>
    <tr>
      <td>{{ KNOWL('artin.conductor',title = "conductor") }}</td>
     <td>
       <input type='text' name='conductor' placeholder="389" size=5/>
     </td>
     <td><span class="formexample"> e.g. 5 or 10-20</span></td>
    </tr>


   <tr>
   <td>
    {{ KNOWL('artin.dimension',title="dimension") }}
    </td>
           <td>
           <input type='text' name='transitive_degree' placeholder="0" size=10>
           </td>
           <td><span class="formexample"> e.g. 0 </span>
           </td>
    </tr>

   <tr>
   <td>
    {{ KNOWL('gg.galois_group',title="Galois group") }}
    </td>
           <td>
           <input type='text' name='group' placeholder="0" size=10>
           </td>
           <td><span class="formexample"> e.g. 0 </span>
           </td>
    </tr>
<tr>
<td align=left colspan=4>Maximum number of Artin representations to display <input type='text' name='count' value=100 size=10>
</td>
</tr>
  </table>
  

<td><button type='submit' value='Search'>Search</button></td>
</form>

    <br>
    This index/search page is not done. The main reason is that it is not fully clear to me yet how people might want to search on Artin representations.
    
    <br>
    Searches that should be allowed:
        
        <UL>
            <LI> based on dimension of representation
            <LI> based on degree of the group action
            <LI> based on conductor
            <LI> based on group name
            <LI> based on size of the group
            <LI> character values?
        </UL>

    <br>
    If you have an opinion, let me (Paul) know!

Meanwhile, here are some examples. You can browse more of them by directly changing the url, or by accessing them from the number field pages (bottom).
However, the database only include a very thin slice of the data that will be available in the end, so it s likely you will follow broken links. 

<table>
    <tr><td><a href = {{url_for('.by_data', dim=1,conductor=1,index=1)}}>Artin representation of dimension 1, conductor 1 and index 1</a></td></tr>
    <tr><td><a href = {{url_for('.by_data', dim=1,conductor=17,index=1)}}>Artin representation of dimension 1, conductor 17 and index 1</a></td></tr>
    <tr><td><a href = {{url_for('.by_partial_data', dim=1,conductor=17)}}>Artin representations of dimension 1 and conductor 17 </a></td></tr>
    <tr><td><a href = {{url_for('.by_data', dim = 3, conductor = 113337, index = 1 )}}>Artin representation of dimension 3, conductor 1133337 and index 1</a></td></tr>
    <tr><td><a href = {{url_for('.by_partial_data', dim=1,conductor=1)}}>Artin representations of dimension 1 and conductor 1 </a></td></tr>
    <tr><td><a href = {{url_for('.by_partial_data', dim=2,conductor=22356)}}>Artin representations of dimension 2 and conductor 22356 </a></td></tr>
    <tr><td><a href = {{url_for('.by_partial_data', dim=4,conductor=136480336)}}>Artin representations of dimension 4 and conductor 136480336 </a></td></tr>
    
</table>
{% endif %}
{% if not user_is_authenticated %}
    Please log in to see more
{% endif %}

{% endblock %}
